114 DISSERTATION SECOND. [pahti. 



Aii invention, in which Hooke has certainly the priority 

 to any one, is the application of a spiral spring to regulate 

 the balance of a watch. It is well known of what practi- 

 cal utility this invention has been found, and how much it 

 has contributed to the solution of the problem of finding the 

 longitude at sea, to which not only he, but Galileo and 

 Huygens, appear all to have had an eye. 



In what respects the theory of motion, Huygens has 

 still another strong claim to our notice. This arises from 

 his solution of the problem of finding the centre of oscilla- 

 tion of a compound pendulum, or the length of the simple 

 pendulum vibrating in the same time with it. Without 

 the solution of this problem, the conclusions respecting the 

 pendulum were inapplicable to the construction of clocks, 

 in which the pendulums used are of necessity compound. 

 The problem was by no means easy, and Huygens was 

 obliged to introduce a principle which had not before been 

 recognised, that if the compound pendulum, after descend- 

 ing to its lowest point, was to be separated into particles 

 distinct and unconnected with one another, and each left, 

 at liberty to continue its own vibration, the common centre 

 of gravity of all those detached weights would ascend to 

 the same height to which it would have ascended had they 

 continued to constitute one body. The above principle 

 Jed him to the true solution, and his investigation, though 

 less satisfactory than those which have been since given, 

 does great credit to his ingenuity. This was the most 

 difficult mechanical inquiry which preceded the invention 

 of the differential or fluxionary calculus. 



2. Hfdrostaticks. 



While the theory of motion, as applied to solids, was 

 thus extended, in what related to fluids, it was making 



